Both a Function and Its Derivative Are Given $f ( x ) = x - 9 x ^ { 2 / 3 } + 7 \quad f ^ { \prime } ( x ) = \frac { x ^ { 1 / 3 } - 6 } { x ^ { 1 / 3 } }$

question 8

Multiple Choice

Both a function and its derivative are given. Use them to find all critical numbers. $f ( x ) = x - 9 x ^ { 2 / 3 } + 7 \quad f ^ { \prime } ( x ) = \frac { x ^ { 1 / 3 } - 6 } { x ^ { 1 / 3 } }$

• A) \(x = 0\)
• B) \(x = 216\)
• C) \(x = 0 , x = - 101\)
• D) \(x = 0 , x = 216\)
• E) \(x = - 101 , x = 216\)

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Definitions:

Position

In a general sense, the location or placement of an object or entity; in data analysis, it might refer to the rank or order of a data point within a dataset.

Area

The extent or measurement of a surface or piece of land.

Standard Normal Random Variable

A type of random variable with a mean of 0 and a standard deviation of 1, used in Z-tests.

Standard Deviation

A measure of the dispersion or variability of a set of values, indicating how much they deviate from the mean.